What is the solution for 2xy+6x+(x^2-4)(dy)/(dx)=0 ?

The solution for 2xy+6x+(x^2-4)(dy)/(dx)=0 is y=(c_{1})/(x^2-4)-3

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2xy+6x+(x^2-4)(dy)/(dx)=0

2 x y + 6 x + (x^{2} - 4) \frac{d y}{d x} = 0

y = \frac{c _{1}}{x ^{2} - 4} - 3

Solution steps

2 x y + 6 x + (x^{2} - 4) \frac{d y}{d x} = 0

Solve separable ODE:

y = \frac{c _{1}}{x ^{2} - 4} - 3

y = \frac{c _{1}}{x ^{2} - 4} - 3

\frac{d y}{d x} = \frac{6 - x ^{2}}{2 y ^{3}}

\frac{d y}{d x} = \frac{x}{y}, y (0) = - 6

\frac{d y}{d x} = 10 x sec (y)

\frac{d y}{d x} = 2 (x^{2}) (y^{2})

\frac{d x}{d t} = x^{2} + \frac{1}{64}

What is the solution for 2xy+6x+(x^2-4)(dy)/(dx)=0 ?
The solution for 2xy+6x+(x^2-4)(dy)/(dx)=0 is y=(c_{1})/(x^2-4)-3